A contact manifold is a manifold equipped with a distribution of codimension
one that satisfies a `maximal non-integrability' condition. A standard example
of a contact structure is a strictly pseudoconvex CR manifold, and operators of
analytic interest are the tangential Cauchy-Riemann operator and the Szego
projector onto its kernel. The Heisenberg calculus is the natural
pseudodifferential calculus developed originally for the analysis of these
operators.
We introduce a `non-integrability' condition for a distribution of arbitrary
codimension that directly generalizes the definition of a contact structure. We
call such distributions polycontact structures. We prove that the polycontact
condition is equivalent to the existence of generalized Szego projections in
the Heisenberg calculus, and explore geometrically interesting examples of
polycontact structures.Comment: 13 pages. Second version contains major revisio